In data compression and noise removal processing on a digital signal, such as an image or a phonetic sound, transformation from discrete signals to frequency domain signals is often used. For example, JPEG (Joint Photographic Experts Group) uses the following steps:                Divide an image (still image) into blocks of a preset size.        Perform a discrete cosine transform (DCT) on each of the blocks to transform it from the spatial domain to the frequency domain.        Quantize signal components in the frequency domain to reduce information, and then perform the entropy coding using Huffman coding. These steps achieve compression (reduction in data amount).        
JPEG-based compression achieves data compression having small influence against original images by performing quantization after the discrete cosine transform (DCT) to concentrate the signal's major energies on a low-frequency domain.
JPEG2000 uses a discrete wavelet transform (DWT) instead of the discrete cosine transform (DCT) (like JPEG, JPEG2000 performs entropy coding after transformation from the spatial domain to the frequency domain and quantization).
A wavelet transform separates each pixel value of an image into a low frequency component and a high frequency component. While the low-frequency component relatively preserves color information in the original image, the areas containing high-frequencies retain a portion which has a sharp transition in pixel values in the image, i.e., edge information of an object. A high-frequency component may include a noise component as well as the edge information of the image. Here, noise means color signals or the like mixed into an image caused by electric currents flowing between adjacent pixels when an image of an object is taken by an imaging device such as a CCD (Charge Coupled Device). The noise (referred to as “camera noise”) arising from imaging devices appears on an image in the form of a distinct granular dot composed of several pixels. Thus, camera noise is often separated as a high-frequency component through wavelet transform processing. The camera noise is color information which is not inherent in the imaged object. Therefore it is preferable to remove the camera noise in order to obtain an image of the object with high fidelity.
The Wavelet Shrinkage method, which is a noise removal method employing a wavelet transform, is disclosed in, for example, Non-Patent Literature NPL 1. The Wavelet Shrinkage method is a method of removing noise by mainly utilizing the facts:                that a noise component is separated as a high-frequency component through a wavelet transform; and        that the camera noise is represented by signal values relatively weaker than that of the edge information inherent in the object.        
As imaging devices improve in performance, images taken in high-sensitivity mode tend to produce much more camera noise. Thus, removing camera noise is becoming more important.
On the other hand, by improvement in quality as imaging devices improves in performance (e.g., sensitivity and resolution), calculation resources, such as memory capacity, and calculation time, which are required for noise removal, are tend to increase.
For example, in the Wavelet Shrinkage method, removing noise processing by a multi-resolution analysis where a plurality of wavelet transforms are carried out is generally used. This multi-resolution analysis is a technique used to cope with the problem that it is not possible to remove a noise component existing in a low-frequency component because a noise component is separated as a high-frequency component. In the multi-resolution analysis, among four components (i.e. one low-frequency component and three high-frequency components), into which an image is divided by a first wavelet transform, representing the resolution level 1, a wavelet transform is carried out on the low-frequency component, which results in the resolution level 2 and in seven divided domains. In this way, dividing is repeated so that the resolution level becomes higher. This makes it possible to remove low-frequency noise which is not possible to be separated by one wavelet transform.
FIG. 1 is an explanatory diagram illustrating a common art related to the Wavelet Shrinkage method employing the multi-resolution analysis. In the example illustrated in FIG. 1, a first coring processing unit 12 performs what is called wavelet shrinkage processing in which coring is performed on the high-frequency component separated from the input signal (original image) by the first wavelet-transform-processing unit 11, by threshold processing on wavelet expansion coefficients (for example, a coefficient whose absolute value is smaller than a threshold is replaced by 0). The result of wavelet shrinkage processing performed by the first coring-processing unit 12 is inputted to the first inverse-wavelet-transform-processing unit 13 (the coring processing unit is referred to also as “wavelet shrinkage processing unit”). The low-frequency component produced through separation by the first wavelet transform processing unit 11 is inputted to the second wavelet transform processing unit 14 to be separated into one low-frequency component and high-frequency components (images with resolutions (multi-resolutions) of different components are generated), and on the high-frequency components wavelet shrinkage is carried out by the second coring processing unit 15. The low-frequency component produced through separation by the second wavelet transform processing unit 14 and an output signal from the second coring processing unit 15 are inputted to the second inverse wavelet-transform processing unit 16. The result of an inverse wavelet transform performed by the second inverse wavelet transform-processing unit 16 is inputted to the first inverse wavelet transform-processing unit 13, and an output signal on which noise removal processing (denoise processing) is performed is outputted from the first inverse wavelet transform-processing unit 13. In this way, when the multi-resolution analysis is applied, different processes is performed on each component produced through separation by the first wavelet-transform-processing unit 11. Data has to be temporarily stored to match the timing of inputs to the first inverse-wavelet-transform-processing unit 13.
In the example (comparative example described later) shown in FIG. 2, a storage device 17 stores the data (an output from the first coring processing unit 12) after the wavelet shrinkage processing.
When the noise removal processing based on a multi-resolution analysis is implemented by a hardware circuit designed for real-time stream processing, the noise removal through wavelet shrinkage based on the multi-resolution analysis is able to be achieved by locating the storage device 17 shown in FIG. 2 as a buffer.
To improve performance of the noise removal based on the multi-resolution analysis, the number of wavelet transforms has to be increased. However, as the number of wavelet transforms increases, the deviation of timing for data input to the final inverse wavelet transform processing (the first inverse-wavelet-transform-processing unit 13 in FIG. 2) gets larger, more data is required to be stored in the storage device 17.
Therefore, to achieve much higher performance of noise removal through wavelet shrinkage, much larger storage capacity (e.g., the capacity of the storage device 17 in FIG. 2) is needed.
As noise components increase due to improvement of imaging devices in sensitivity, required performance of noise removal is becoming higher. At the same time, reduction in storage capacity of a storage device (e.g., the storage device 17 in FIG. 2) is also required.
Patent Literature PTL 1, which is a result of the related art literature search carried out by the applicant, discloses an imaging device which enables reduction in line memory significantly compared with the case where wavelet transforms are separately performed on the brightness signal and the color difference signal after these signals are generated. The imaging device according to PTL 1 includes a wavelet processing unit which performs wavelet transform processing, coring processing, and inverse wavelet transform processing on image signals. The wavelet processing unit includes: a wavelet decomposition processing unit which performs a wavelet transform on an image signal composed of a plural color signals; and a plurality of coring processing units which suppress signals satisfying different conditions after the wavelet transform, wherein the line memory directly stores the image signal composed of the plural color signals arranged in a preset arrangement, and the wavelet decomposition processing unit performs the wavelet transform on the image data stored in the line memory. Patent Literature PTL 2 discloses a configuration of: inputting an original image consisting of a plurality of pixels; decomposing the inputted image through multi-resolution conversion to generate a plurality of low-frequency images having sequentially lowering frequencies and high-frequency images having corresponding sequentially lowering frequencies; performing noise removal processing on each of the plurality of low-frequency images and the plurality of high-frequency images, which are generated; and obtaining a noise-removed image from the original image based on both results of the noise-removed low-frequency images and the noise-removed high-frequency images. Patent Literature PTL 3 discloses a noise reduction process in which a wavelet transforms is used as a technique of multi-resolution conversion. The noise reduction is achieved by carrying out a wavelet transform on original image data to obtain a plurality of frequency-band components, and then performing coring processing on each of the frequency-band components. The disclosed is obtaining image data on which noise-reduction processing is performed by recomposing, through an inverse wavelet transform, frequency-band components after coring processing, and generating corrected video signals by performing n-stage multi-resolution composition of a high-frequency component and a low-frequency component on which correction processing is performed. Patent Literature PTL 4 discloses an image processing device which: converts, by a coring processing unit, signals of very small amplitude in sub-band image signals including a high-frequency component transformed by a wavelet transform processing unit to 0; and, by an inverse wavelet transform processing unit, restores two image signals by composing a sub-band image signal which includes a low-frequency signal component and a sub-band image signal on which coring processing is performed in combination of different normal or reverse phases, synthesizes the two image signals at a certain phase, and outputs an edge waveform in an output image signal as an edge waveform in rotational symmetry. This consequently makes it possible to perform coring processing to reduce noise while suppressing blurred edges and phase shifting caused by the coring.